Interactions between cold rubidium Rydberg atoms with external control

We explore the interactions in an ensemble of $^{87}$Rb atoms at temperatures ~500 $\mu$K excited to the 50S$_{1/2}$ Rydberg state. The atoms interact with an externally-controlled static electric field, producing a Stark-shifted energy level and an induced electric dipole moment. Changes in this induced dipole moment give rise to increased interactions between the atoms, as evidenced by a suppression of the excitation to the Rydberg state. We model this excitation suppression with a simple Monte Carlo simulation and show that the suppression of excitation is fully explained by a dipole-dipole interaction between the induced dipoles along with the van der Waals interaction. Additionally, we investigate a perturbative approach to calculate the full interactions by using Stark-perturbed wavefunctions in a calculation of the van der Waals interaction through Forster processes.